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lim(x->oo) [(1)/(1times2)+(1)/(2times3)...

`lim_(x->oo) [(1)/(1times2)+(1)/(2times3)+(1)/(3times4)+.....+(1)/(n(n+1))]`

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[(1)/(1times2)+(1)/(2times3)+(1)/(3times4)+......+(1)/(99times100)] =

lim_(n rarr oo) ((1)/(1.2) + (1)/(2.3) + (1)/(3.4) +…..+ (1)/(n(n+1))) is :

lim_ (n rarr oo) [(1) / (1.2) + (1) / (2.3) + (1) / (3.4) + ... + (1) / (n (n + 1))] =

underset(n to oo)lim {(1)/(1.2)+(1)/(2.3)+(1)/(3.4)+...+(1)/(n(n+1))}=

lim_(nto oo) {(1)/(n+1)+(1)/(n+2)+(1)/(n+3)+...+(1)/(n+n)} is, equal to

lim_(nto oo) {(1)/(n+1)+(1)/(n+2)+(1)/(n+3)+...+(1)/(n+n)} is, equal to

lim_ (n rarr oo) ((1) / (n + 1) + (1) / (n + 2) + (1) / (n + 3) + ...... + (1) / (6n ))

lim_(n rarr oo){(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+....+(1)/((2n+1)(2n+3 ))